from Modern Latin tendo Achillis, first used by German surgeon Lorenz Heister (1683-1758) and so-called in reference to the one vulnerable spot of the Greek hero Achilles, whose mother held him by the heel when she dipped him in the River Styx to render him invulnerable (this story is not in Homer and not found before 1c. C.E.). Earlier Achilles' sinew, from Modern Latin chorda Achillis, coined 1693 by Dutch anatomist Philip Verheyden when dissecting his own amputated leg. Hence figurative use of heel of Achillies for "vulnerable spot" (1810).
Greek hero of the Trojan War stories, bravest, swiftest, and handsomest of Agamemnon's army before Troy, he was son of Thetis and Peleus. His name is perhaps a compound of akhos "pain, grief" (see awe) + laos "the people, a people" (see lay (adj.)); or else it is from Pre-Greek (non-IE). Related: Achillean.
early 14c., acheven, "to perform, execute, accomplish;" late 14c., "gain as a result of effort," from Old French achever (12c.) "to finish, accomplish, complete," from phrase à chef (venir) "at an end, finished," or Vulgar Latin *accapare, from Late Latin ad caput (venire); both the French and Late Latin phrases meaning literally "to come to a head," from ad "to" (see ad-) + stem of Latin caput "head" (from PIE root *kaput- "head").The Lat. caput, towards the end of the Empire, and in Merov[ingian] times, took the sense of an end, whence the phrase ad caput venire, in the sense of to come to an end .... Venire ad caput naturally produced the Fr. phrase venir à chef = venir à bout. ... From this chief, O.Fr. form of chef (q.v.) in sense of term, end, comes the Fr. compd. achever = venir à chef, to end, finish. [Auguste Brachet, "An Etymological Dictionary of the French Language," transl. G.W. Kitchin, Oxford, 1878] Related: Achieved; achieving.
1580s, fabled river of the Lower World in Greek mythology, from Greek Akheron, the name of several real rivers in addition to being the mythical river of the Underworld. The name perhaps means "forming lakes" (compare Greek akherousai "marsh-like water"), from PIE root *eghero- "lake" (source of Lithuanian ežeras, ažeras, Old Prussian assaran, Old Church Slavonic jezero "lake"). The derivation from Greek akhos "woe" is considered folk etymology. The name later was given to certain rivers in Greece and Italy because they flowed through dismal surroundings or disappeared underground and were thought to be gateways to the Underworld. Related: Acherontic.
Middle English aken, from Old English acan "suffer continued pain," from Proto-Germanic *akanan, which is perhaps from a PIE root *ag-es- "fault, guilt," with apparent cognates in Sanskrit and Greek, which itself is perhaps imitative of groaning. Originally the verb was pronounced "ake," the noun "ache" (as in speak/speech). The noun changed its pronunciation to conform to the verb, but the spelling of both was changed to ache c. 1700 on a false assumption of a Greek origin (specifically Greek akhos "pain, distress," which rather is a distant relation of awe (n.)). Related: Ached; aching.